Network regularization on TCGA Cancer Data

1 Overview

Data

• TCGA project: prad.data.2018.10.11
• Tissue type: primary.solid.tumor
  • Only using coding genes
• Subtract survival time: Using survival time from diagnostics
• Degree calculation: string

Normalization

• LOG2 transform: yes
• Gene by gene: center

Model options

• Train / Test: 80%
• Model (Alpha / Target variables): glmnet (0.60 / 3), hub (0.10 / 13), orphan (0.10 / 5)

Network processing

• Degree calculation: string
• Edge cutoff: 0
• Unweighted edges

cor/cov method: pearson

• only applies if network type is correlation/covariance

2 Load and normalize data

Data

• TCGA project: prad.data.2018.10.11
• Tissue type: primary.solid.tumor
  • Only using coding genes
• Degree calculation: string
• Subtract survival time: ****

Normalization

• LOG2 transform: yes
• Gene by gene: center

2.1 Load TCGA data

See prepare.tcga.survival.data function for how to configure parameters.

This uses data packages from obtained from ‘github:averissimo/tcga’ that contain FPKM expression levels.

prepare.tcga.survival.data('prad.data.2018.10.11',
                           'primary.solid.tumor',
                            normalization        = 'center',
                            log2.pre.normalize   = TRUE,
                            handle.duplicates    = 'keep_first',
                            coding.genes         = TRUE,
                            subtract.surv.column = '')

2.1.1 Summary of data

## [INFO]        Loaded data from TCGA: prad.data.2018.10.11
## [INFO]               type of tissue: primary.solid.tumor
## [INFO]   observations (individuals): 445 (10 event / 435 censored)
## [INFO]            variables (genes): 19850

2.1.2 Survival curve

2.2 Load degree data

Network processing

• Degree calculation: string
• Edge cutoff: 0
• Unweighted edges

cor/cov method: pearson

• only applies if network type is correlation/covariance

2.3 Preparing degree vector

• Normalize degree between 0 and 1
• Hub: heuristic( 1 - degree )
• Orphan: heuristic( degree )
• trans.fun is a double power to scale the values

see ?glmSparseNet::heuristicScale or ?glmSparseNet::hubHeuristic

# see ?glmSparseNet::heuristic.scale
trans.fun <- function(x) {
    heuristicScale(x) + 0.2
}

2.3.1 Genes with degree above 4000

ensembl_gene_id	degree	external_gene_name
ENSG00000150991	10394	UBC
ENSG00000170325	6346	PRDM10
ENSG00000100300	5797	TSPO
ENSG00000174775	5614	HRAS
ENSG00000142208	5573	AKT1
ENSG00000111640	5363	GAPDH
ENSG00000163631	5260	ALB
ENSG00000177606	4952	JUN
ENSG00000141510	4936	TP53
ENSG00000197122	4903	SRC
ENSG00000254647	4592	INS
ENSG00000112062	4187	MAPK14
ENSG00000170315	4114	UBB
ENSG00000170345	4010	FOS

2.3.2 Original degree frequency

Original

LOG10 Scale on X-axis

3 Model Inference

3.1 Train and test sets

## [INFO] Size of sets: (size/events)
##  * Train: 80.00% ::  356 /    8
##  *  Test: 20.00% ::   89 /   2

## [INFO] Number of variables per model:

Model	BaseModel	Alpha	TargetVars	nvars
Elastic Net	Elastic Net	0.60	3	4
Hub	Elastic Net	0.60	3	3
Orphan	Elastic Net	0.60	3	3
Elastic Net	Hub	0.10	13	14
Hub	Hub	0.10	13	13
Orphan	Hub	0.10	13	14
Elastic Net	Orphan	0.10	5	6
Hub	Orphan	0.10	5	5
Orphan	Orphan	0.10	5	5

## [INFO] note, selected variables could be slightly different from target, to have more accuracy increase nlambda in code

4 Results

4.1 Relative risk distribution

Calculated using the inferred models and the train/test datasets. The higher the better.

Test Set

Train Set

4.2 Kaplan-Meier Curves

4.2.1 Models on test sets

Elastic Net (base model: Elastic Net)

Test set

Training set

Hub (base model: Elastic Net)

Test set

Training set

Orphan (base model: Elastic Net)

Test set

Training set

Elastic Net (base model: Hub)

Test set

Training set

Hub (base model: Hub)

Test set

Training set

Orphan (base model: Hub)

Test set

Training set

Elastic Net (base model: Orphan)

Test set

Training set

Hub (base model: Orphan)

Test set

Training set

Orphan (base model: Orphan)

Test set

Training set

4.3 Summary Table

weighted	penalization	project	tissue	cutoff	coding.genes	alpha	model	nvars	km.train	km.test	c.index.train	c.index.test
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.60	Elastic Net	4	0.0082306	0.1434727	0.8864542	0.1860465
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.60	Hub	3	0.0783487	0.9784762	0.6932271	0.3488372
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.60	Orphan	3	0.2083740	0.4942273	0.8390093	-1.0000000
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Elastic Net	14	0.0039942	0.1868517	0.9063745	0.3023256
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Hub	13	0.0292004	0.9784762	0.7898406	0.4651163
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Orphan	14	0.0434207	0.1100129	0.9143426	0.7209302
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Elastic Net	6	0.0054774	0.1868517	0.8605578	0.2093023
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Hub	5	0.0344144	0.9596664	0.7360558	0.3837209
FALSE	string	prad.data.2018.10.11	primary.solid.tumor	0	TRUE	0.10	Orphan	5	0.0260847	0.5987003	0.8624128	0.6119403

4.4 Non-zero genes

4.4.1 Venn Diagram of selected genes

4.4.1.1 Overlap between models (with same target number of variables)

Base model: Elastic Net with Target Vars: 3 and Alpha: 0.60

Base model: Hub with Target Vars: 13 and Alpha: 0.10

Base model: Orphan with Target Vars: 5 and Alpha: 0.10

Table of genes in models

(not running at the moment)

4.5 Hallmarks of Cancer links

5 5000 Runs

5.1 C-Index distribution

Test set

Summary of C-Index and Log-rank

metric	model	base.model	target.vars	alpha	mean	std	median	min
C-Index (Test set)	Hub	Elastic Net	3	0.60	0.337	0.678	0.557	-1
C-Index (Test set)	Hub	Hub	13	0.10	0.328	0.680	0.554	-1
C-Index (Test set)	Hub	Orphan	5	0.10	0.295	0.683	0.472	-1
C-Index (Test set)	Elastic Net	Elastic Net	3	0.60	-0.214	0.864	-1.000	-1
C-Index (Test set)	Elastic Net	Hub	13	0.10	0.542	0.344	0.619	-1
C-Index (Test set)	Elastic Net	Orphan	5	0.10	0.091	0.778	0.397	-1
C-Index (Test set)	Orphan	Elastic Net	3	0.60	-0.254	0.819	-1.000	-1
C-Index (Test set)	Orphan	Hub	13	0.10	0.570	0.358	0.655	-1
C-Index (Test set)	Orphan	Orphan	5	0.10	0.377	0.524	0.554	-1
Log-rank (Test set)	Hub	Elastic Net	3	0.60	0.447	0.340	0.305	0.0143
Log-rank (Test set)	Hub	Hub	13	0.10	0.453	0.344	0.305	0.00855
Log-rank (Test set)	Hub	Orphan	5	0.10	0.453	0.347	0.304	0.0101
Log-rank (Test set)	Elastic Net	Elastic Net	3	0.60	0.439	0.264	0.406	0.000311
Log-rank (Test set)	Elastic Net	Hub	13	0.10	0.421	0.314	0.298	0.0126
Log-rank (Test set)	Elastic Net	Orphan	5	0.10	0.471	0.290	0.378	0.00701
Log-rank (Test set)	Orphan	Elastic Net	3	0.60	0.475	0.260	0.495	0.000608
Log-rank (Test set)	Orphan	Hub	13	0.10	0.433	0.320	0.290	0.0244
Log-rank (Test set)	Orphan	Orphan	5	0.10	0.464	0.325	0.317	0.0143

C-Index Distribution

Rank

Elastic Net vs Hub

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.0376236
Hub with target nvars: 13 alpha: 0.10	0.1037840
Orphan with target nvars: 5 alpha: 0.10	0.0666755

Elastic Net vs. Orphan

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.6595686
Hub with target nvars: 13 alpha: 0.10	0.4239360
Orphan with target nvars: 5 alpha: 0.10	0.1549383

Hub vs. Orphan

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.0140233
Hub with target nvars: 13 alpha: 0.10	0.1039123
Orphan with target nvars: 5 alpha: 0.10	0.0916150

Train set

Summary of C-Index and Log-rank

metric	model	base.model	target.vars	alpha	mean	std	median	min
C-Index (Train set)	Hub	Elastic Net	3	0.60	0.766	0.085	0.777	0.398
C-Index (Train set)	Hub	Hub	13	0.10	0.812	0.050	0.812	0.63
C-Index (Train set)	Hub	Orphan	5	0.10	0.700	0.066	0.705	0.445
C-Index (Train set)	Elastic Net	Elastic Net	3	0.60	0.764	0.074	0.781	0.472
C-Index (Train set)	Elastic Net	Hub	13	0.10	0.878	0.040	0.878	0.741
C-Index (Train set)	Elastic Net	Orphan	5	0.10	0.767	0.076	0.769	0.5
C-Index (Train set)	Orphan	Elastic Net	3	0.60	0.781	0.057	0.792	0.519
C-Index (Train set)	Orphan	Hub	13	0.10	0.867	0.048	0.877	0.651
C-Index (Train set)	Orphan	Orphan	5	0.10	0.750	0.136	0.788	0.298
Log-rank (Train set)	Hub	Elastic Net	3	0.60	0.066	0.072	0.038	0.000407
Log-rank (Train set)	Hub	Hub	13	0.10	0.021	0.032	0.011	0.000271
Log-rank (Train set)	Hub	Orphan	5	0.10	0.094	0.080	0.077	6e-04
Log-rank (Train set)	Elastic Net	Elastic Net	3	0.60	0.355	0.243	0.308	0.00251
Log-rank (Train set)	Elastic Net	Hub	13	0.10	0.025	0.030	0.012	0.000303
Log-rank (Train set)	Elastic Net	Orphan	5	0.10	0.284	0.268	0.193	0.000734
Log-rank (Train set)	Orphan	Elastic Net	3	0.60	0.358	0.240	0.306	1.54e-13
Log-rank (Train set)	Orphan	Hub	13	0.10	0.058	0.080	0.040	0.000671
Log-rank (Train set)	Orphan	Orphan	5	0.10	0.197	0.208	0.098	0.000965

C-Index Distribution

C-Index Rank

5.2 Log-rank test on Kaplan-Meier models

5.2.1 Log-Rank distribution

Cumulative

Distribution of Log-rank test with groups separated by high and low risk groups

Distribution

Distribution of Log-rank test with groups separated by high and low risk groups

5.2.2 Log-Rank Rank

5.2.2.1 Elastic Net vs Hub

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.0214725
Hub with target nvars: 13 alpha: 0.10	0.0371328
Orphan with target nvars: 5 alpha: 0.10	0.0113305

5.2.2.2 Elastic Net vs. Orphan

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.2178867
Hub with target nvars: 13 alpha: 0.10	0.0000101
Orphan with target nvars: 5 alpha: 0.10	0.0058999

5.2.2.3 Hub vs. Orphan

base.model	r.squared
Elastic Net with target nvars: 3 alpha: 0.60	0.0005798
Hub with target nvars: 13 alpha: 0.10	0.0004029
Orphan with target nvars: 5 alpha: 0.10	0.0005280

5.3 Consesus genes

5.3.1 Selected genes over all runs

Bar plots of frequencies

Overlap between variables selected

Base model: Elastic Net with Target Vars: 3 and Alpha: 0.60

Base model: Hub with Target Vars: 13 and Alpha: 0.10

Base model: Orphan with Target Vars: 5 and Alpha: 0.10

5.3.2 Selected genes in significant runs

i.e. with pvalue < 0.05 in Log-rank test using the test set.

Bar plots of frequencies

Overlap between variables selected

5.3.2.0.1 Base model Elastic Net with target nvars: 0.60 alpha: 3

5.3.2.0.2 Base model Hub with target nvars: 0.10 alpha: 13

5.3.2.0.3 Base model Orphan with target nvars: 0.10 alpha: 5

5.3.3 Genes in Significant runs

i.e. with pvalue < 0.05 in Log-rank test using the test set.

Top consensus 20 genes

Gene	Overlap	total
ENSG00000278674	2	571
PRR27	2	571
GAGE2A	2	395
DEFA1	2	241
UBC	1	218
SRC	1	218
PRDM10	1	184
INS	1	137
CDK2	1	125
AKT1	1	101
UMPS	1	65
TP53	1	61
RAD51	1	49
GAPDH	1	48
MYC	1	44
CSN2	2	38
ASPDH	2	38
FOS	1	36
AC068946.1	2	33
UBB	1	31

All Genes

_{^{ENSG00000278674(571), PRR27(571), GAGE2A(395), DEFA1(241), UBC(218), SRC(218), PRDM10(184), INS(137), CDK2(125), AKT1(101), UMPS(65), TP53(61), RAD51(49), GAPDH(48), MYC(44), CSN2(38), ASPDH(38), FOS(36), AC068946.1(33), UBB(31), CABS1(29), MIA-RAB4B(29), CDK1(28), LIPN(26), PRKCG(26), MAPK3(25), POTEI(25), CACNG3(24), NUTM2F(20), LHX5(19), NRAS(17), PCSK9(16), NKX1-2(14), ELOVL3(14), HSP90AA1(13), CCDC150(12), AC006486.1(11), KRTAP19-3(10), NUTM2F(10), GSK3A(9), HRAS(8), SLC5A10(7), KRTAP19-7(7), LHX5(7), ACTRT2(7), SLC25A47(6), PCSK9(6), CACNG3(5), OR2T35(5), OR2T2(5), FBXO47(5), ITGA2B(5), RPS6KB1(5), OR2T35(5), TPTE(4), SPINK6(3), MTCP1(3), GAS2(3), PCDHA8(3), MAGEC3(2), OR2W5(2), TARM1(2), AC104581.2(2), RHOA(2), PRSS53(2), FGF11(2), OR2T2(2), CDK3(2), MAGEA9B(2), ENSG00000183791(1), CDC42(1), MAPK1(1), MYB(1), THRSP(1), OR4S1(1), KRTAP10-8(1), ASPDH(1), POM121L12(1), NKX1-2(1), KRTAP19-3(1), PRSS51(1), AC104581.2(1), OR1S1(1)}}

5.4 Best C-index test in all runs

Best Elastic Net model (C-Index test)

[INFO] Coefs. list

[1] “CACNG3, DEFA1, LHX5, OR4S1”

Test set

Full set

Best Hub model (C-Index test)

[INFO] Coefs. list

[1] “AKT1, CDK2, PRDM10, SRC, UBC”

Test set

Full set

Best Orphan model (C-Index test)

[INFO] Coefs. list

[1] “ENSG00000278674, GAGE2A, PRR27”

Test set

Full set

5.5 Best Log-rank test in all runs

Best Elastic net (Log-rank test)

[INFO] Coefs. list

[1] “DEFA1, ENSG00000278674, PRR27”

Test set

Full set

Best Hub model (Log-rank test)

[INFO] Coefs. list

[1] “CDK2, FOS, GAPDH, INS, MAPK3, MYC, PRDM10, PRKCG, RAD51, SRC, TP53, UBC, UMPS”

Test set

Full set

Best Orphan model (Log-rank test)

[INFO] Coefs. list

[1] “DEFA1, ENSG00000278674, GAGE2A, PRR27”

Test set

Full set

NULL

6 Parameters for the report

## [INFO]          balanced.sets: TRUE
## [INFO]        calc.params.old: FALSE
## [INFO]           coding.genes: TRUE
## [INFO]     degree.correlation: pearson
## [INFO]          degree.cutoff:       0.000
## [INFO]            degree.type: string
## [INFO]      degree.unweighted: TRUE
## [INFO]      handle.duplicates: keep_first
## [INFO]                   log2: TRUE
## [INFO]                n.cores:      14.000
## [INFO]          normalization: center
## [INFO]                 ntimes:    5000.000
## [INFO]                project: prad.data.2018.10.11
## [INFO]                   seed:    1985.000
## [INFO]                 subset: Inf
## [INFO]   subtract.surv.column: (I do not know how to display this)
## [INFO]            target.vars: list(alpha = 0.6, vars = 3), list(alpha = 0.1, vars = 13), list(alpha = 0.1, vars = 5)
## [INFO]                 tissue: primary.solid.tumor
## [INFO]                  train:       0.800